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# Refer to the figure and find the volume generated by rotating the given region about the specified line.$\Re_1$ about $OA$

## $\frac{1}{3} \pi$

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Applications of Integration

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### Video Transcript

I've got a question here where we need to refer the figure in the textbook. So when you're looking at that figure, um, you open up the textbook and see it and you'll see that was asking us to do is find the volume generated by rotating the given region about a specified line are so one about Oh A If you look at 02 a, the X Y is just from 0 to 0, but you're X goes from 0 to 1 because you're oh, this point, you're you're on your a this point 10 So here, when you were to solve for your volume, you would take the integral from zero one and we took the area integrated with respect to X. Yeah, we know that it's a cone. So the area of a circle, it's the same thing that pi r squared your ex. Okay. And here we know that you're are is your ex value. You have pi X. Where defense. Alright, When you integrate this, you'll get I X cubed over three 120 which would be pi over three, right. And that will be your final answer for the volume as our is rotated about. Oh, a Well, I hope that clarifies the question. Thank you so much for watching

The University of Texas at Arlington

#### Topics

Applications of Integration

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